by Dr Adrian Worton
A fortnight ago, UK Prime Minister Theresa May called a snap General Election. Her intention to do was deliberately kept top secret in order to gain an advantage over opponents. Unfortunately, it also means that we were caught out; whilst our 2015 model allowed for detailed analysis, we had significant upgrades planned for a presumed 2020 election.
However, we have been able to make some small tweaks to present a new-and-improved version for this year! In this article we will explain how it is calculated, and present our first set of results.
A fortnight ago, UK Prime Minister Theresa May called a snap General Election. Her intention to do was deliberately kept top secret in order to gain an advantage over opponents. Unfortunately, it also means that we were caught out; whilst our 2015 model allowed for detailed analysis, we had significant upgrades planned for a presumed 2020 election.
However, we have been able to make some small tweaks to present a new-and-improved version for this year! In this article we will explain how it is calculated, and present our first set of results.
Individual seat probabilities
The starting point of the model is to find the probabilities of winning an individual seat for each party involved. We will be using the same method as before, however we will go over it again here. You can follow the explanation by following the example in the slideshow below (use the arrow keys to cycle between figures).
The starting point of the model is to find the probabilities of winning an individual seat for each party involved. We will be using the same method as before, however we will go over it again here. You can follow the explanation by following the example in the slideshow below (use the arrow keys to cycle between figures).
| | Firstly, we start with the odds for that seat (Fig. 1a), which we convert to decimal (Fig. 1b), which we'll refer to as a. Any party whose odds are longer than 50/1 for that seat are removed from consideration. We then invert the odds by dividing 1 by (a+1) (the rationale for which is explained here). We will refer to the inverted odds as b (Fig. 1c). |
In order to improve the chances of the favourite winning, which we found necessary to match real-life results, we raise each value of b to the power of 1.8 (Fig. 1d). We then divide each party's value by the total to give a final probability (Fig. 1e).
Applying swing
Previously, we assumed that each seat's result was independent of each other. This is, of course, a false assumption; a factor which affects the result of a seat in Liverpool is likely to have also had an effect on a seat in London. For example, it is probably fair to say that more voters are influenced by party leaders than by their own constituency candidates for those same parties, despite the fact that those individuals will be the ones on the ballot paper.
Applying swing
Previously, we assumed that each seat's result was independent of each other. This is, of course, a false assumption; a factor which affects the result of a seat in Liverpool is likely to have also had an effect on a seat in London. For example, it is probably fair to say that more voters are influenced by party leaders than by their own constituency candidates for those same parties, despite the fact that those individuals will be the ones on the ballot paper.
| To incorporate this in the model, each party within the model is given a 'swing' score. This is a random value somewhere between 0.5 and 2.0. This is used when calculating individual seat probabilities. Specifically, the inverted odds are multiplied by each party's swing score. The examples to the right demonstrate how the swing scores can affect the final probabilities. | |
Crucially, the same swing scores are applied to every constituency. For example, if Labour's swing score is 1.50, then this value is used in every seat.
Overall results
To generate a simulation of the full country, the result of each seat is randomly generated according to the probabilities given. We can simply add up all the winning parties to find the seat totals for each party.
You can try out the full simulator yourself on our dedicated 2017 General Election page.
Predictions
Using this model, we can give our first set of predictions. Firstly, we can get the expected seat total for each party by simply adding up the total number of probabilities of that party winning across all 650 seats.
So for example, were there only three seats, and the probability of the Conservatives winning those seats were 95%, 30%, 5%, 85% and 65%, then their expected seat count would be:
Overall results
To generate a simulation of the full country, the result of each seat is randomly generated according to the probabilities given. We can simply add up all the winning parties to find the seat totals for each party.
You can try out the full simulator yourself on our dedicated 2017 General Election page.
Predictions
Using this model, we can give our first set of predictions. Firstly, we can get the expected seat total for each party by simply adding up the total number of probabilities of that party winning across all 650 seats.
So for example, were there only three seats, and the probability of the Conservatives winning those seats were 95%, 30%, 5%, 85% and 65%, then their expected seat count would be:
0.95 + 0.30 + 0.05 + 0.85 + 0.65 = 2.80
The table below gives the expected seat count for all the parties within our model:
Party |
Current seats |
Expected seats |
Conservatives |
330 |
395.33 |
Labour |
230 |
163.54 |
SNP |
54 |
46.68 |
Liberal Democrats |
9 |
20.26 |
DUP |
8 |
8.13 |
Sinn Féin |
4 |
5.73 |
Plaid Cymru |
3 |
3.91 |
SDLP |
3 |
1.64 |
Ulster Unionists |
2 |
1.00 |
Greens |
1 |
1.48 |
UKIP |
0 |
0.81 |
Independents & other parties |
6 |
1.51 |
We can see that our model agrees with the media consensus that we are heading to a Tory landslide, with an expected 394 seats, 69 seats higher than the threshold needed for a majority. Meanwhile, Labour are anticipated to crash significantly below the 200 seat barrier. It should be noted that Labour have taken at least 200 seats in all elections since the Second World War (they took 154 in the 1935 General Election).
Elsewhere, the Liberal Democrats are anticipated to bounce back from their shock two years ago, whilst the SNP are expected to keep a strong grip on Scottish seats, albeit not to the same extent as before.
Whilst these predictions give us a measure of strength for each party, the model is probability-based, so we also want to know the potential spread of seats. To this end, the model was run 5000 times, with the seat counts for each of the main four parties recorded. Below you can see histograms showing their spread of seats:
Elsewhere, the Liberal Democrats are anticipated to bounce back from their shock two years ago, whilst the SNP are expected to keep a strong grip on Scottish seats, albeit not to the same extent as before.
Whilst these predictions give us a measure of strength for each party, the model is probability-based, so we also want to know the potential spread of seats. To this end, the model was run 5000 times, with the seat counts for each of the main four parties recorded. Below you can see histograms showing their spread of seats:
The smallest ray of hope for anti-Tory parties is that in some cases, they failed to reach a majority. However, this constituted just 0.4% of simulations. In exactly 99% of cases the Conservatives managed to increase their majority, and in a healthy 41.6% of simulations they managed over 400 seats.
The current record for seats held in the Commons is 418, set by Tony Blair's 1997 victory. Our model gives Theresa May's Conservatives a 18.4% chance of beating this.
The current record for seats held in the Commons is 418, set by Tony Blair's 1997 victory. Our model gives Theresa May's Conservatives a 18.4% chance of beating this.
The news only gets worse for Jeremy Corbyn and Labour. The single-highest seat count they get across the 5000 simulations is 231, which is still 82 fewer than the very lowest count for the Conservatives. As noted above, a total less than 200 would be a historically poor performance for Labour, and there is a 92.2% chance of this happening.
For Nicola Sturgeon's SNP, it is likely the only way is down after the remarkable success of 2015 - particularly after losing their majority in last year's Scottish elections. That said, there is a 1.7% chance of increasing their seat count (it should be noted that the SNP are on two seats fewer than in 2015 due to two MPs resigning the whip). It appears that a seat total in the 40s is most likely (66.8% likely, in fact), however there is a reasonable chance of a total in the 50s. Even in the worst-case scenario seen in the simulations, 30 out of 59 is still a majority across Scotland.
Tim Farron should be very confident of improving his party's representation in parliament, with 94.6% chance of this happening. However, matching 2010's relative success of 57 seats appears out of reach. A tally somewhere between the mid-10s and the mid-20s seems the most likely scenario currently.
Summary
The model presented here has numerous uses, many of which were demonstrated two years ago. Over the following weeks, we will be going in-depth into the model to bring new perspectives on this election.
The main advantage of such a method of looking at the election is that the full range of results can be given. This is in contrast to many places, where their predictions consist solely of their predicted seat counts, with no sense of how variable they are.
Looking at the current output, it appears we are heading for a Conservative win of the scale of Tony Blair's 1997 triumph. However, the model is entirely dependent on bookies' odds, which in turn are based on opinion polls. This meant that the 2015 model's predictions were somewhat out, and could be out again (although we've tried to broaden the prediction ranges to improve this).
Finally, a reminder that our dedicated General Election 2017 page has the full model for you to try simulations of, as well as profiles of each constituency in the country.
Summary
The model presented here has numerous uses, many of which were demonstrated two years ago. Over the following weeks, we will be going in-depth into the model to bring new perspectives on this election.
The main advantage of such a method of looking at the election is that the full range of results can be given. This is in contrast to many places, where their predictions consist solely of their predicted seat counts, with no sense of how variable they are.
Looking at the current output, it appears we are heading for a Conservative win of the scale of Tony Blair's 1997 triumph. However, the model is entirely dependent on bookies' odds, which in turn are based on opinion polls. This meant that the 2015 model's predictions were somewhat out, and could be out again (although we've tried to broaden the prediction ranges to improve this).
Finally, a reminder that our dedicated General Election 2017 page has the full model for you to try simulations of, as well as profiles of each constituency in the country.
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